An accelerated Picard method for nonlinear systems related to variably saturated flow

In this paper, we investigate the effectiveness of the Anderson acceleration method applied to modified Picard iteration for nonlinear problems arising in variably saturated flow modeling. While many authors have studied the relative merits of Newton’s method and modified Picard iteration in this context, the combination of Anderson acceleration and modified Picard iteration has not been investigated for these problems until recently. Since modified Picard iteration can be slow to converge, we investigate the use of Anderson acceleration to provide faster convergence while maintaining the robustness and lower memory requirements of modified Picard iteration relative to Newton’s method. Results indicate that Anderson acceleration significantly improves not only convergence speed but also robustness of modified Picard iteration and can often provide faster solutions than Newton’s method without the need for derivative computations.

► We investigate effectiveness of Anderson acceleration applied to modified Picard. ► Compared to Newton method, Anderson provides faster convergence and more robustness. ► Anderson accelerated modified Picard requires only symmetric linear solves. ► Results show Anderson often provides faster solutions than Newton’s method.